| Abstract: |
| We introduce a new nonlocal model for gravitational fingering and study its wave propagation dynamics. Gravitational fingering is an instability in the displacement of miscible fluids in porous media, governed by Darcy`s law, which occurs when a lighter fluid lies below a heavier one and gravity drives an exchange of positions. Our main result establishes the existence of a propagating terrace consisting of infinitely many traveling waves in a semi-discrete Transverse Flow Equilibrium (TFE) model. The talk is based on ongoing joint work with Sergey Tikhomirov (PUC-Rio, Brazil) and extends earlier results on two-tubes models of gravitational fingering (SIMA, arxiv:2401.05981) |
|